Find the smallest positive angle $x$ that satisfies $\sin 2x \sin 3x = \cos 2x \cos 3x,$ in degrees.
Solution: From the given equation,
\[\cos 2x \cos 3x - \sin 2x \sin 3x = 0.\]Then from the angle addition formula, $\cos (2x + 3x) = 0,$ or $\cos 5x = 0.$  To find the smallest positive solution, we take $5x = 90^\circ,$ so $x = \boxed{18^\circ}.$